The model in (REF ) at any \(Z_T \ne 0\)  is equivalent to the model in (REF ).
The term added to the Kähler potential of the VA theory in [1]} is of the form \(Z_T T \bar{T}\) . To make it canonical one had to rescale it so that
\(Z_T T \bar{T} \rightarrow T\bar{T}\) . Therefore the couplings of the form \(TX^2\)  was rescaled as \(TX^2 \rightarrow {1\over Z_T^{1/2} } TX^2\) . The vertex involving the \(T\) -scalar and 2 fermions of the \(X\)  superfield and a vertex involving the scalar from the \(X\)  multiplet with fermions from the \(T\)  and \(X\)  multiplets blow up in the limit \(Z_T \rightarrow 0\) .
Already in this simple model we see the issues with the claim in [1]} that the model where \(T\)  is a propagating field is equivalent to a model where \(T\)  is a Lagrange multiplier.
